Distributed Least Product Relative Error estimation for semi-parametric multiplicative regression with massive data

Distributed systems have been widely used for massive data analysis, but few studies focus on multiplicative regression models. We consider a communication-efficient surrogate likelihood method using the Least Product Relative Error criterion for semi-parametric multiplicative models on massive datasets. The non-parametric component is efficiently handled via B-spline approximation. We derive the asymptotic properties for both parametric and non-parametric components, while the SCAD and adaptive Lasso penalty functions are developed and their oracle properties for variable selection are validated. Simulation studies and an application to an energy prediction dataset are used to demonstrate the effectiveness and practical utility of the proposed method.